1 Math CAMPPP 2011 Breakout Session 1: Algebraic Thinking

2 Learning Goals I will understand the three key patterning concepts (additive, multiplicative, and algebraic thinking). I will identify the mathematics necessary to respond to students in the moment. 2

Fish Pond The fish pond is a central place for sharing. If you have a question, please “fish” for an answer by posting your question in the pond. If you have an idea you can share with others, please “bank” it on the side. 3

What’s Your Number?? In your math journal, record a three-digit number that represents you in some way. (For example, Cathy’s might be 323 because she has 3 children and has been married 23 years.) Also in your journal, please record a personal goal or two for Math CAMPPP. 4

What’s Your Number? Please share your number with your fishing buddies at your table. As a group, come up with a three-digit number that represents your group. Also create a group goal for the week. Please record both of these on chart paper. 5

Something to Hang Your Hat On …or to hang on your hat… Please share your group number, then individually introduce yourself using your personal number. Please use pipe cleaners to create your three- digit number to attach to your fishing hat.. 6

Before/Part 1/Minds On: A Few Quiet Moments What did you hear in the breakout sessions with Ruth and Cathy that resonated with you, or gave you a different perspective? Please jot down a few notes in your journal. 7

During/Part 2/Action: Problem Solving With a partner, please complete the following problem about Pattern Kingdom on chart paper. 8

Pattern Kingdom In the Pattern Kingdom, each city is connected to the other cities by a road. To make it simple for people to get around, there is a road connecting each city with all of the other cities. When the Pattern Kingdom only had 3 cities, there were 3 roads to connect them. 9

Pattern Kingdom When the Pattern Kingdom grew to 4 cities, there were 6 roads to connect them so that there was a direct route from any city to any other city. Now the Pattern Kingdom has 14 cities. How many roads does it have? What if there were 32 cities? How many roads would there be? Is there a rule? How did you figure it out? Can you give evidence? 10

After/Part 3/Consolidation We will use a Bansho for sharing our collective thinking Please use the LNS Bansho monograph for your own professional reading. 11

After/Part 3/Consolidation Working with a grade-level partner, please reflect and discuss the following two questions: 1.What math do you see in this problem? 2.Where do you see this math in our Ontario curriculum? 12

Responding in the Moment Math-talk in class: encourage justifications of generalizations –Encourage explanations using generic examples –Encourage justifications with respect to how calculations relate to the students’ interpretation of the problem context Activities that allow for students to connect rules with visual representations increase the likelihood of student success Discussions about the limitations of focusing on particular values

Furthering Student Thinking Variation – hold one variable the same and vary the other For example, in the cube sticker problem, what if the rods were made of –Hexagonal prisms? –Octagonal prisms? What is varied? What stays the same? If students understand the connection between their rule and the original problem context, then this understanding can easily be transferred to new situations

Fishing for Your Thoughts It matters not how many fish are in the sea if you don't have any bait on your hook. -Anonymous Today’s symbol for your fishing hat is a hook. Please reflect on the following questions, and jot your thoughts down on a fish: What hooked you today? What do you still need to know about the three algebraic representations? 15